nipunbatra/adaboost.pynb

## adaboost.pynb
{
 "metadata": {
  "name": "AdaBoost"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Initially we plot the training samples according to their classes on x1,x2 plane."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "train=array([[1,3],[1,1],[2,1],[2,2],[2,3],[3,3]])\n",
      "y=array([1,1,-1,-1,1,-1])\n",
      "bool_y=array(y==1)\n",
      "x1=array([i[0] for i in train])\n",
      "x2=array([i[1] for i in train])\n",
      "pos_index=y==1\n",
      "x1_pos=x1[pos_index]\n",
      "x2_pos=x2[pos_index]\n",
      "neg_index=~pos_index\n",
      "x1_neg=x1[neg_index]\n",
      "x2_neg=x2[neg_index]\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1')\n",
      "ylabel('x2');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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LW8bYj8ZiPWVt+5HUFrCesjLu43E8P/J5thVsUxhIv6YWmtcL9VTuNqfTScGG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\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we list down 8 resultant possible classifiers from the given 4 decision stumps and plot the same."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 1: x1>=1.5\n",
      "hold(True)\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([1.5,1.5,1.5,1.5,1.5],[0,1,2,3,4]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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LSTmbAhe6OEEDpNSksPSxpabWJdIdFAgi1+jfvz+bX99M8vHkzodCAySfSGbz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\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 2: x1>=2.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([2.5,2.5,2.5,2.5,2.5],[0,1,2,3,4]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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1qSx9YqmpdYn4gwJB5Cr9+/dn8xubSTme0vVQaISUEylsfn1zQPVFEPGUAkHk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\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 3: x2>=1.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([0,1,2,3,4],1.5*ones(5));\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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UtfVHUlvAesrK2I/H8vyI59lWsE1hIL2aWmheL9RTucucTicFGwrYUb6DusY6\nLnKREEKICo9iaop6Kktw8ee9U4EgInIN8ee9U4eMREQEUCCIiIibAkFERAAFgoiIuCkQREQEUCCI\niIibAkFERAAFgoiIuCkQREQEUCCIiIibAkFERAAFgoiIuCkQREQECFAgbN26lZEjRxIfH8+LL77Y\narvD4aB///4kJyeTnJzM0qVLA1GGiIh0QojZE7pcLhYtWsSOHTuIjY3l7rvvJiMjg1GjRnmNS0tL\no7i42OxvLyIiXWT6HkJFRQXDhw9n6NChhIaGMnfuXN55551W49TrQEQkuJi+h3Dy5Eni4uI8z4cM\nGUJ5ebnXGIvFwr59+0hMTCQ2Npbly5eTkJDQaq7c3FzPf9vtduzq+CUi4sXhcOBwOEyZy/RAsFgs\nHY4ZN24c1dXV2Gw2tmzZwuzZszl69GircVcGgoiItPbdP5bz8vK6PJfph4xiY2Oprq72PK+urmbI\nkCFeYyIiIrDZbADMmDEDp9PJmTNnzC5FREQ6wfRAGD9+PMeOHaOqqorm5mY2bNhARkaG15ja2lrP\nOYSKigoMw2DgwIFmlyIiIp1g+iGjkJAQVq1axX333YfL5WLBggWMGjWKNWvWAJCTk8PGjRtZvXo1\nISEh2Gw2ioqKzC5DREQ6yWIE6cd9LBaLPokkItJJ/rx36kplEREBFAgiIuKmQBAREUCBICIibgoE\nEREBFAgiIuKmQBAREUCBICIibgoEEREBFAgiIuKmQBAREUCBICIibgoEEREBFAgiIuKmQBAREUCB\nICIibgoEEREBFAgiIuKmQPCTw+Ho6RJ8ojrN0xtqBNVptt5Spz8CEghbt25l5MiRxMfH8+KLL7Y5\nZvHixcTHx5OYmMiBAwcCUUa36C3/SFSneXpDjaA6zdZb6vSH6YHgcrlYtGgRW7dupbKyksLCQj75\n5BOvMSUlJRw/fpxjx46xdu1aFi5caHYZIiLSSaYHQkVFBcOHD2fo0KGEhoYyd+5c3nnnHa8xxcXF\nZGdnA5CSksLZs2epra01uxQREekMw2Rvv/228eijj3qeFxQUGIsWLfIaM2vWLOO9997zPJ8yZYqx\nf/9+rzGAHnrooYceXXh0VQgms1gsPo279J7f/td9d7uIiASW6YeMYmNjqa6u9jyvrq5myJAhVx1T\nU1NDbGys2aWIiEgnmB4I48eP59ixY1RVVdHc3MyGDRvIyMjwGpORkUF+fj4AZWVlDBgwgJiYGLNL\nERGRTjCQEciDAAAFZUlEQVT9kFFISAirVq3ivvvuw+VysWDBAkaNGsWaNWsAyMnJYebMmZSUlDB8\n+HDCwsJYt26d2WWIiEhndfnsg0m2bNlifO973zOGDx9uvPDCC22Oefzxx43hw4cbY8eONT788MNu\nrvCSjurctWuXcdNNNxlJSUlGUlKS8fzzz3d7jY888ogRHR1t3Hnnne2OCYa17KjOYFhLwzCML774\nwrDb7UZCQoIxevRoY+XKlW2O6+k19aXOnl7T8+fPGxMmTDASExONUaNGGb/61a/aHNfTa+lLnT29\nlle6ePGikZSUZMyaNavN7Z1dzx4NhIsXLxp33HGH8fnnnxvNzc1GYmKiUVlZ6TVm8+bNxowZMwzD\nMIyysjIjJSUlKOvctWuXkZ6e3u21XWnPnj3Ghx9+2O4bbTCspWF0XGcwrKVhGMapU6eMAwcOGIZh\nGA0NDcaIESOC8t+nL3UGw5o2NTUZhmEYTqfTSElJMfbu3eu1PRjW0jA6rjMY1vKyFStWGPPmzWuz\nnq6sZ4/euqK3XLPgS53Q85+MmjhxIpGRke1uD4a1hI7rhJ5fS4BBgwaRlJQEQHh4OKNGjeLLL7/0\nGhMMa+pLndDza2qz2QBobm7G5XIxcOBAr+3BsJa+1Ak9v5Zw6cM4JSUlPProo23W05X17NFAOHny\nJHFxcZ7nQ4YM4eTJkx2Oqamp6bYa26vhu3VaLBb27dtHYmIiM2fOpLKysltr9EUwrKUvgnEtq6qq\nOHDgACkpKV6vB9uatldnMKxpS0sLSUlJxMTEMGnSJBISEry2B8tadlRnMKwlwC9+8Qteeukl+vRp\n+228K+vZo4Fg1jULgebL9xs3bhzV1dV89NFHPP7448yePbsbKuu8nl5LXwTbWjY2NvKTn/yElStX\nEh4e3mp7sKzp1eoMhjXt06cPBw8epKamhj179rR5b6BgWMuO6gyGtXz33XeJjo4mOTn5qnsrnV3P\nHg2E3nLNgi91RkREeHY1Z8yYgdPp5MyZM91aZ0eCYS19EUxr6XQ6mTNnDg8//HCbv/jBsqYd1RlM\na9q/f3/uv/9+9u/f7/V6sKzlZe3VGQxruW/fPoqLixk2bBiZmZns3LmT+fPne43pynr2aCD0lmsW\nfKmztrbWk8YVFRUYhtHmsceeFAxr6YtgWUvDMFiwYAEJCQk8+eSTbY4JhjX1pc6eXtP6+nrOnj0L\nwPnz59m+fTvJycleY4JhLX2ps6fXEmDZsmVUV1fz+eefU1RUxOTJkz1rd1lX1tP06xA6o7dcs+BL\nnRs3bmT16tWEhIRgs9koKirq9jozMzPZvXs39fX1xMXFkZeXh9Pp9NQYDGvpS53BsJYA7733HuvX\nr2fs2LGeN4Vly5bxxRdfeGoNhjX1pc6eXtNTp06RnZ1NS0sLLS0tZGVlMWXKlKD7Xfelzp5ey7Zc\nPhTk73pajGA4XS4iIj1OHdNERARQIIiIiJsCQUREAAWCiIi4KRBEumD69OlERkaSnp7e06WImEaB\nINIF//Ef/0FBQUFPlyFiKgWCyFW8//77JCYmcuHCBZqamrjzzjuprKxk8uTJbd7GQqQ369EL00SC\n3d13301GRgbPPvss58+fJysrq9XNzkSuFQoEkQ785je/Yfz48dx444288sorPV2OSMDokJFIB+rr\n62lqaqKxsZHz5897Xg/GO8WK+EOBINKBnJwcli5dyrx583j66ac9r+uuL3Kt0SEjkavIz8/nhhtu\nYO7cubS0tPD973+fXbt28dxzz3HkyBEaGxuJi4vjjTfeYNq0aT1drohfdHM7EREBdMhIRETcFAgi\nIgIoEERExE2BICIigAJBRETcFAgiIgLA/wdFH0ODZ6/XywAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 4: x2>=2.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([0,1,2,3,4],2.5*ones(5));\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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D9ZS19UdSW8B6ysrYj8fy/Ijn2VawTWEgvZpaaF4v1FO5y5xOJwUbCthRvoO6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\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 5: x2>=1.5 and x1>=1.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([1.5,1.5,2.5,4],[4,1.5,1.5,1.5]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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EDZBSk8LSx5aaWpdIV1AgiFyjf//+bH59M8nHkzseCg2QfCKZza9tVl8E6ZEU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\nQIEgIiLNFAgiIgLA/wc2K2mFmzI9nQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 6: x2>=2.5 and x1>=1.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([4,1.5,1.5,1.5],[2.5,2.5,2.5,4]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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oNELSiSQ2v7ZZfRGkT1IgiHxHSEgIO97cQcrnKVjrvDvJbK21knIyhR1v7lA/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\ngg==\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 7: x2>=2.5 and x2>=1.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([4,2.5,2.5,2.5],[2.5,2.5,2.5,4]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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LIL2SAkHkOyIiItj+5nbSPk/DWu/dSWZrnZW0E2lsf3O7+iFIr6VAEGlHREQE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\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 8: x2>=2.5 and x1>=1.5\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([4,1.5,1.5,1.5],[1.5,1.5,1.5,4]);\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "legend(('Postive','Negative'))\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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EDZBSk8LSx5aaWpdIV1AgiFyjf//+bH59M8nHkzseCg2QfCKZza9tVl8E6ZEU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\nQIEgIiLNFAgiIgLA/wc2K2mFmzI9nQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "According to AdaBoost Algorithm, at each iteration we pick up a base classifier which gives the minimum misclassification error. Thus, the next step is to find the same amongst these 8 classifiers. Each point is also given the same weight for the first iteration. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D=1.0/len(train)*ones(len(train))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "From observation we can see that the first classifier will give the least misclassification error. We next find the error in classifier #1."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 1 predicts 'Negative' if x1>=1.5 and 'Positive' otherwise\n",
      "classifier_1_pred=array(train[:,0]<1.5)\n",
      "misclassify_1_count=sum(classifier_1_pred!=bool_y)\n",
      "classifier_1_out=-1*np.ones(len(y))\n",
      "for i in range(0,len(y)):\n",
      "    if classifier_1_pred[i]==True:\n",
      "        classifier_1_out[i]=1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print misclassify_1_count"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that in this classifier only 1 sample was misclassified. By manual observation, from the plots we made earlier showing different classifiers, classifier #1 should be chosen for the first iteration. Since all the weights at this stage were equal, we didn't need to take them into consideration. Next we see which point was misclassified. Thus, we have $$\\epsilon_t=0.1667$$ .It is a positive point which was misclassified (2,3). Thus, its weight would be increased for the next iteration. We now calculate $$\\alpha_t = 0.5*log(1-\\epsilon_t/\\epsilon_t)$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "alpha_1=0.5*math.log((1-.1667)/.1667)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "0.8045989658157064"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we need to update the weights as per: $$D_{t+1}(i)=D_t(i)*exp(-\\alpha_t*y_i*h_t(x_i))/Z_t$$\n",
      "Initially we calculate the weights and leave normalization for next step."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(D)):\n",
      "    print D[i],y[i],classifier_1_out[i]\n",
      "    D[i]=D[i]*math.exp(-1*alpha_1*y[i]*classifier_1_out[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.166666666667 1 1.0\n",
        "0.166666666667 1 1.0\n",
        "0.166666666667 -1 -1.0\n",
        "0.166666666667 -1 -1.0\n",
        "0.166666666667 1 -1.0\n",
        "0.166666666667 -1 -1.0\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "array([ 0.07454454,  0.07454454,  0.07454454,  0.07454454,  0.37263328,\n",
        "        0.07454454])"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus, we see that at this stage, the 5th point, which was misclassified, has an incremented weight. Next, we normalize the weights.\n",
      "$$Z_t=sum(D)$$\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z_t=sum(D)\n",
      "D=(1.0/z_t)*D\n",
      "print \"Updated weights after first iteration\",D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Updated weights after first iteration [ 0.100012  0.100012  0.100012  0.100012  0.49994   0.100012]\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we reflect this set of weight changes in the original plot. \n",
      "NB: For weight=1/6, Marker size =20"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(y)):\n",
      "    if y[i]==1:\n",
      "        #Point belonging to positive class\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'r+',ms=20*D[i]/.1667)\n",
      "    else:\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'go',ms=20*D[i]/.1667)\n",
      "xlim(0,4)\n",
      "ylim(0,4)\n",
      "xlabel('x1');\n",
      "ylabel('x2');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRCEAAKIoBACAJAoBABBFIQAAJEn/D+JbjL4VOHLmAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we try to ensure that the point which was misclassified previously is learnt in this iteration, which would come as a consequence of it being assigned higher weight.From observation, we can see that classfier #4 would give the minimum error, $$\\epsilon_t$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 4 predicts 'Positive' if x2>=2.5 and 'Negative' otherwise\n",
      "classifier_4_pred=array(train[:,1]>2.5)\n",
      "misclassify_4_count=sum(classifier_4_pred!=bool_y)\n",
      "classifier_4_out=-1*np.ones(len(y))\n",
      "for i in range(0,len(y)):\n",
      "    if classifier_4_pred[i]==True:\n",
      "        classifier_4_out[i]=1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "misclassify_4_count"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus, although 2 samples have been misclassifed, sample number 5 which had highest weight has been correctly classified. We calculate error for this iteration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "epsilon_2=2*D[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_2=math.log((1-epsilon_2)/epsilon_2)\n",
      "print alpha_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.38614437987\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we again update the weights as we did after the first iteration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(D)):\n",
      "    D[i]=D[i]*math.exp(-1*alpha_2*y[i]*classifier_4_out[i])\n",
      "print D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.02500675  0.399988    0.02500675  0.02500675  0.12500375  0.399988  ]\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we normalize the weights.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z_t=sum(D)\n",
      "D=(1.0/z_t)*D\n",
      "print \"Updated weights after second iteration\",D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Updated weights after second iteration [ 0.02500675  0.399988    0.02500675  0.02500675  0.12500375  0.399988  ]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(y)):\n",
      "    if y[i]==1:\n",
      "        #Point belonging to positive class\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'r+',ms=20*D[i]/.1667)\n",
      "    else:\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'go',ms=20*D[i]/.1667)\n",
      "xlim(0,4)\n",
      "ylim(0,4)\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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VlpZq7dq1evPNN/vd4TXXXKOcnBxJUmJiorKystTQ0BA2pry8vKtU8vLy1NzcrMbGxuH8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\n/w9/1ZK7KH5D+AAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus, after the second iteration, we see that now 2 points have much more weights than the other ones. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now see that classifier 2 will give the least weighted error and thus we use it for next iteration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Classifier 2 predicts 'Negative' if x1>=2.5 and 'Positive' otherwise\n",
      "classifier_2_pred=array(train[:,0]<2.5)\n",
      "misclassify_2_count=sum(classifier_2_pred!=bool_y)\n",
      "classifier_2_out=-1*np.ones(len(y))\n",
      "for i in range(0,len(y)):\n",
      "    if classifier_2_pred[i]==True:\n",
      "        classifier_2_out[i]=1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "misclassify_2_count"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The two samples which have been misclassified have their weights as 0.025, thus, we have\n",
      "$$\\epsilon_3=2*.025=.05$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "epsilon_3=.05\n",
      "alpha_3=math.log((1-epsilon_3)/epsilon_3)\n",
      "print alpha_3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2.94443897917\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(D)):\n",
      "    D[i]=D[i]*math.exp(-1*alpha_2*y[i]*classifier_2_out[i])\n",
      "print D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.00625263  0.100012    0.100012    0.100012    0.03125562  0.100012  ]\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z_t=sum(D)\n",
      "D=(1.0/z_t)*D\n",
      "print \"Updated weights after third iteration\",D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Updated weights after third iteration [ 0.01428988  0.22856947  0.22856947  0.22856947  0.07143224  0.22856947]\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(0,len(y)):\n",
      "    if y[i]==1:\n",
      "        #Point belonging to positive class\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'r+',ms=20*D[i]/.1667)\n",
      "    else:\n",
      "        plt.plot(train[:,0][i],train[:,1][i],'go',ms=20*D[i]/.1667)\n",
      "xlim(0,4)\n",
      "ylim(0,4)\n",
      "xlabel('x1');\n",
      "ylabel('x2');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since the problem specified us to do only 3 iterations, we stop at this point. Next, we need to combine the three classifiers according to the following rule:\n",
      "$$H(x)=sgn(\\displaystyle\\sum_{t=1}^{3}\\alpha_th_t(x))$$\n",
      "We have:\n",
      "$$H(x)=sgn(0.8046*(1.5-x1)+1.386*(x2-2.5)+2.944*(2.5-x1))$$\n",
      "or\n",
      "$$H(x)=sgn(5.2-3.75x1+1.4x2)$$\n",
      "We now plot this classifier and compare this with the Decision Tree classifier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subplot(1,2,1)\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "adaboost_x2=np.linspace(0,4,1000)\n",
      "adaboost_x1=(1.4*adaboost_x2+5.2)/3.75\n",
      "plt.plot(adaboost_x1,adaboost_x2,'y')\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "xlabel('x1');\n",
      "ylabel('x2');\n",
      "title('ADABoost')\n",
      "subplot(1,2,2)\n",
      "plt.plot(x1_pos,x2_pos,'r+',ms=20)\n",
      "plt.plot(x1_neg,x2_neg,'go',ms=20)\n",
      "plt.plot([1.5,1.5,1.5,1.5,1.5],[0,1,2,3,4],'k')\n",
      "plt.plot([2.5,2.5,2.5],[2.5,3.5,5],'k')\n",
      "plt.plot([1.5,2.5,4],[2.5,2.5,2.5],'k')\n",
      "\n",
      "xlim(0,4);\n",
      "ylim(0,4);\n",
      "title('Complex Decision Tree')\n",
      "xlabel('x1');\n",
      "ylabel('x2');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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baWjI5/0HjDGTuCG4me79B3z9IsZYX9wQ3EhnZw00mlr4+yeIXQpjzAFxQ3Aj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\nvsFgsd4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is compared to the classifier generated by the Decision Trees. We see that the point (2,2) is misclassified by the ensemble classifier. However, it is expected that as the number of iterations of ADABoost will increase our classifier will improve. This is based on the fact that there is no noise in the dataset. To further illustrate this, we can see the reduction in error with iteration count."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import rc\n",
      "rc('text', usetex=True)\n",
      "rc('font', family='serif')\n",
      "rc('font', size=12)\n",
      "epsilon_vector=np.array([.1667,epsilon_2,epsilon_3])\n",
      "iteration_vector=np.array([1,2,3])\n",
      "plt.plot(iteration_vector,epsilon_vector)\n",
      "plt.title(r'Error in $\\epsilon_t$ vs iteration t')\n",
      "plt.xlabel(r\"Iteration (t)\");\n",
      "plt.ylabel(r'$\\epsilon_t$');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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TO66VzY5rIqI1qCrwZ38G/PCHzZuVzdFNREQNdPKklpUtCM2Zlc3RTUREDaRn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\n"
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}